浙江大学学报（理学版）2026，Vol.53Issue(1)：88-96,9.DOI:10.3785/1008-9497.25033
基于物理信息神经网络求解带自由边界条件的DCIS问题
Solving DCIS problem with free boundary conditions based on physical information neural network
摘要
Abstract
Solving the ductal carcinoma in situ(DCIS)problem with free boundary conditions can better reveal the changing law of Ductal Carcinoma in situ,mean while reducing the cost of experiments and improving the accuracy of numerical results.This paper exploits physics-informed neural networks(PINNs)to solve the problem of ductal carcinoma in situ with free boundary conditions.We construct two independent deep neural networks to respectively approximate the nutrient concentration and the free boundary,the loss function is represented by the residuals of the partial differential equations,initial and boundary conditions,and solved using the Adam optimization algorithm.In order to verify the accuracy and computational efficiency of the solution of the free boundary problem by PINNs,numerical simulation was performed.The results not only show the effectiveness of PINNs in solving the problem,but also verify that the numerical solution agrees well with the exact solution.关键词
原位管癌/物理信息神经网络/自由边界条件/数值模拟Key words
DCIS/PINNs/free boundary conditions/numerical simulation分类
轻工纺织引用本文复制引用
CAI Yunhan,GE Meibao..基于物理信息神经网络求解带自由边界条件的DCIS问题[J].浙江大学学报（理学版）,2026,53(1):88-96,9.基金项目
国家自然科学基金项目(12371428) （12371428）
浙江省教育厅一般科研项目(Y202559822). （Y202559822）
